First of all, as shown in figure REF , note that a thread configuration that can lock a specified set of boundary subregions \(\lbrace  A,B,AB, \cdots \rbrace \)  must equivalently lock its corresponding set of RT surfaces \(\lbrace  {\gamma _A},{\gamma _B},{\gamma _{AB}}, \cdots \rbrace  \)  (due to the divergenceless property of bit threads), therefore, we can focus on the latter. A set of non-crossing boundary subregions corresponds to a set of non-intersecting RT surfaces. These RT surfaces divide the bulk spacetime into small cells, whose boundaries are RT surfaces or boundary subregions. As shown in the figure, for the sake of discussion, let us focus on the case where the bulk spacetime is decomposed into only two kinds of basic cells. One is the three-sided cell whose boundary is composed of three adjacent RT surfaces, and the other is the two-sided cell whose boundary is composed of an RT surface and a corresponding boundary subregion. Note that other types of cells containing more sides can always return to the case we considered by adding more auxiliary RT surfaces [1]}.
